Properties

Conductor 8041
Order 560
Real No
Primitive Yes
Parity Even
Orbit Label 8041.fs

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(8041)
 
sage: chi = H[41]
 
pari: [g,chi] = znchar(Mod(41,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8041
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 560
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 8041.fs
Orbit index = 149

Galois orbit

sage: chi.sage_character().galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{8041}(41,\cdot)\) \(\chi_{8041}(90,\cdot)\) \(\chi_{8041}(107,\cdot)\) \(\chi_{8041}(150,\cdot)\) \(\chi_{8041}(193,\cdot)\) \(\chi_{8041}(226,\cdot)\) \(\chi_{8041}(250,\cdot)\) \(\chi_{8041}(299,\cdot)\) \(\chi_{8041}(360,\cdot)\) \(\chi_{8041}(398,\cdot)\) \(\chi_{8041}(403,\cdot)\) \(\chi_{8041}(600,\cdot)\) \(\chi_{8041}(618,\cdot)\) \(\chi_{8041}(623,\cdot)\) \(\chi_{8041}(656,\cdot)\) \(\chi_{8041}(666,\cdot)\) \(\chi_{8041}(772,\cdot)\) \(\chi_{8041}(809,\cdot)\) \(\chi_{8041}(821,\cdot)\) \(\chi_{8041}(838,\cdot)\) \(\chi_{8041}(864,\cdot)\) \(\chi_{8041}(981,\cdot)\) \(\chi_{8041}(1030,\cdot)\) \(\chi_{8041}(1091,\cdot)\) \(\chi_{8041}(1129,\cdot)\) \(\chi_{8041}(1196,\cdot)\) \(\chi_{8041}(1251,\cdot)\) \(\chi_{8041}(1282,\cdot)\) \(\chi_{8041}(1306,\cdot)\) \(\chi_{8041}(1337,\cdot)\) ...

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{11}{16}\right),e\left(\frac{1}{7}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{219}{280}\right)\)\(e\left(\frac{129}{560}\right)\)\(e\left(\frac{79}{140}\right)\)\(e\left(\frac{117}{560}\right)\)\(e\left(\frac{1}{80}\right)\)\(e\left(\frac{53}{80}\right)\)\(e\left(\frac{97}{280}\right)\)\(e\left(\frac{129}{280}\right)\)\(e\left(\frac{111}{112}\right)\)\(e\left(\frac{89}{112}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{560})\)